Details

Time bar (total: 23.9s)

sample140.0ms

Algorithm
intervals
Results
45.0ms256×body80valid
9.0ms256×pre80true

simplify1.1s

Counts
1 → 1
Iterations
IterNodes
done2005
51509
4498
3162
274
137
018

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (cos (* u2 (* 2 PI))) (* (pow (* -2 (log u1)) 0.5) 1/6) 0.5)
0.1b
(pow (* -2 (log u1)) 0.5)
0.3b
(* u2 (* 2 PI))
0.4b
(* (pow (* -2 (log u1)) 0.5) 1/6)

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
20×add-exp-log
12×pow1
11×add-sqr-sqrt add-cbrt-cube
9×prod-exp
8×*-un-lft-identity associate-*l* add-cube-cbrt
4×expm1-log1p-u associate-*r* pow-prod-down pow-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×pow-unpow sqr-pow
2×pow-to-exp unpow-prod-down pow-pow *-commutative unswap-sqr
1×fma-udef
Counts
4 → 78
Calls
4 calls:
0.0ms
(fma (cos (* u2 (* 2 PI))) (* (pow (* -2 (log u1)) 0.5) 1/6) 0.5)
10.0ms
(pow (* -2 (log u1)) 0.5)
24.0ms
(* u2 (* 2 PI))
24.0ms
(* (pow (* -2 (log u1)) 0.5) 1/6)

series2.0s

Counts
4 → 12
Calls
4 calls:
477.0ms
(fma (cos (* u2 (* 2 PI))) (* (pow (* -2 (log u1)) 0.5) 1/6) 0.5)
377.0ms
(pow (* -2 (log u1)) 0.5)
45.0ms
(* u2 (* 2 PI))
1.1s
(* (pow (* -2 (log u1)) 0.5) 1/6)

simplify776.0ms

Counts
90 → 90
Iterations
IterNodes
done2000
21102
1382
0160

prune581.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize73.0ms

Local error

Found 4 expressions with local error:

0.1b
(pow (* -2 (log u1)) 0.5)
0.2b
(* (* (pow (* -2 (log u1)) 0.5) (sqrt 1/6)) (sqrt 1/6))
0.3b
(* u2 (* 2 PI))
0.3b
(* (pow (* -2 (log u1)) 0.5) (sqrt 1/6))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
34×add-exp-log
19×prod-exp
17×add-sqr-sqrt
16×add-cbrt-cube
14×pow1
13×associate-*r*
11×*-un-lft-identity add-cube-cbrt
9×associate-*l*
8×sqrt-prod
7×cbrt-unprod
6×pow-exp
5×pow-prod-down
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp unswap-sqr sqr-pow
3×pow-to-exp pow-unpow *-commutative
2×unpow-prod-down pow-pow
Counts
4 → 98
Calls
4 calls:
7.0ms
(pow (* -2 (log u1)) 0.5)
44.0ms
(* (* (pow (* -2 (log u1)) 0.5) (sqrt 1/6)) (sqrt 1/6))
13.0ms
(* u2 (* 2 PI))
16.0ms
(* (pow (* -2 (log u1)) 0.5) (sqrt 1/6))

series2.7s

Counts
4 → 12
Calls
4 calls:
393.0ms
(pow (* -2 (log u1)) 0.5)
1.2s
(* (* (pow (* -2 (log u1)) 0.5) (sqrt 1/6)) (sqrt 1/6))
55.0ms
(* u2 (* 2 PI))
1.1s
(* (pow (* -2 (log u1)) 0.5) (sqrt 1/6))

simplify803.0ms

Counts
110 → 110
Iterations
IterNodes
done2000
21203
1407
0165

prune712.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (cos (* u2 (* 2 PI))) (* 1/6 (pow (* (pow (log u1) 1.0) (pow -2 1.0)) 0.5)) 0.5)
0.1b
(pow (* (pow (log u1) 1.0) (pow -2 1.0)) 0.5)
0.3b
(* u2 (* 2 PI))
0.4b
(* 1/6 (pow (* (pow (log u1) 1.0) (pow -2 1.0)) 0.5))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
48×add-exp-log
33×prod-exp
32×pow-exp
14×pow-to-exp
11×add-sqr-sqrt add-cbrt-cube
10×pow1
8×*-un-lft-identity add-cube-cbrt
6×associate-*r* associate-*l*
4×expm1-log1p-u pow-prod-down cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×pow-unpow sqr-pow
2×unpow-prod-down pow-pow *-commutative unswap-sqr
1×fma-udef
Counts
4 → 94
Calls
4 calls:
0.0ms
(fma (cos (* u2 (* 2 PI))) (* 1/6 (pow (* (pow (log u1) 1.0) (pow -2 1.0)) 0.5)) 0.5)
12.0ms
(pow (* (pow (log u1) 1.0) (pow -2 1.0)) 0.5)
18.0ms
(* u2 (* 2 PI))
16.0ms
(* 1/6 (pow (* (pow (log u1) 1.0) (pow -2 1.0)) 0.5))

series2.7s

Counts
4 → 12
Calls
4 calls:
524.0ms
(fma (cos (* u2 (* 2 PI))) (* 1/6 (pow (* (pow (log u1) 1.0) (pow -2 1.0)) 0.5)) 0.5)
1.2s
(pow (* (pow (log u1) 1.0) (pow -2 1.0)) 0.5)
54.0ms
(* u2 (* 2 PI))
936.0ms
(* 1/6 (pow (* (pow (log u1) 1.0) (pow -2 1.0)) 0.5))

simplify1.2s

Counts
106 → 106
Iterations
IterNodes
done2001
21344
1501
0204

prune639.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize77.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (pow (* -2 (log u1)) 0.5) (* (pow (* -2 (log u1)) 0.5) 1/216))
0.4b
(* (pow (* -2 (log u1)) 0.5) (* (pow (* -2 (log u1)) 0.5) (* (pow (* -2 (log u1)) 0.5) 1/216)))
0.4b
(* (pow (* -2 (log u1)) 0.5) 1/216)
0.5b
(cbrt (* (pow (* -2 (log u1)) 0.5) (* (pow (* -2 (log u1)) 0.5) (* (pow (* -2 (log u1)) 0.5) 1/216))))

rewrite316.0ms

Algorithm
rewrite-expression-head
Rules
380×add-exp-log
335×prod-exp
134×pow-exp
67×pow-to-exp
20×add-cbrt-cube
15×associate-*l*
11×add-sqr-sqrt
10×cbrt-unprod
8×*-un-lft-identity add-cube-cbrt
5×associate-*r*
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp sqr-pow
3×unpow-prod-down *-commutative
2×unswap-sqr
1×cbrt-prod pow1/3
Counts
4 → 181
Calls
4 calls:
59.0ms
(* (pow (* -2 (log u1)) 0.5) (* (pow (* -2 (log u1)) 0.5) 1/216))
131.0ms
(* (pow (* -2 (log u1)) 0.5) (* (pow (* -2 (log u1)) 0.5) (* (pow (* -2 (log u1)) 0.5) 1/216)))
24.0ms
(* (pow (* -2 (log u1)) 0.5) 1/216)
92.0ms
(cbrt (* (pow (* -2 (log u1)) 0.5) (* (pow (* -2 (log u1)) 0.5) (* (pow (* -2 (log u1)) 0.5) 1/216))))

series4.7s

Counts
4 → 12
Calls
4 calls:
1.5s
(* (pow (* -2 (log u1)) 0.5) (* (pow (* -2 (log u1)) 0.5) 1/216))
1.1s
(* (pow (* -2 (log u1)) 0.5) (* (pow (* -2 (log u1)) 0.5) (* (pow (* -2 (log u1)) 0.5) 1/216)))
1.0s
(* (pow (* -2 (log u1)) 0.5) 1/216)
1.0s
(cbrt (* (pow (* -2 (log u1)) 0.5) (* (pow (* -2 (log u1)) 0.5) (* (pow (* -2 (log u1)) 0.5) 1/216))))

simplify928.0ms

Counts
193 → 193
Iterations
IterNodes
done2004
21209
1461
0196

prune762.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes486.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify5.0ms

Iterations
IterNodes
done22
122
017

end0.0ms

sample2.9s

Algorithm
intervals
Results
2.2s8000×body80valid
417.0ms8000×pre80true